Final answer:
The correct equation that models the path of the ball Jake kicked is y = -x^2 + 150x + 100, which takes into account the specified maximum height and horizontal distance traveled by the ball.
Step-by-step explanation:
The question relates to the field of mathematics and specifically to the part involving projectile motion in physics. Jake kicked the ball in such a way that it traveled a horizontal distance of 150 feet and reached a maximum height of 100 feet. To model the path of the ball, we are looking for an equation of a parabola, which will have a negative coefficient for the x^2 term since the path of the ball is a downward-opening parabola. The equation must also match the given maximum height and range.
Thus, the correct equation that models the trajectory of the ball is option D: y = -x^2 + 150x + 100. This is because at the ball's maximum height (100 feet high), x would be half of the horizontal range, meaning 75 feet. Substituting 75 for x in the equation should yield 100 feet for y. Also, when the ball hits the ground (y=0), x should be 150 feet, which fits the given equation D.